Prerequisites

The calculations were made in R using R-Studio. The structure of the code is essentially based on the structure of the text. The raw code is in the file order_of_code.R. The file extended with Markdown is order_of_code-doc.RMD and the file order_of_code-doc.html is generated from it.

Note: The base path for rmd files is the folder in which they are located, not the r-project. Consequently, order_of_code.R and order_of_code-doc.RMD are both located in the root folder of the project.

Depending on the hardware, the subsequent code can run for several hours or even a few days.

Install “Just Another Gibbs Sampler” (JAGS) (Plummer, 2003) if you want to run the Bayesian analyses anew. Version 4.3 - as used here - can be downloaded in pre-compiled form for a number of OS here: https://sourceforge.net/projects/mcmc-jags/ . The manual can be found here: https://people.stat.sc.edu/hansont/stat740/jags_user_manual.pdf

The code makes extensive use of the function source to call external code. Thus, the main part of the code remains slim, well structured and readable.

Install required packages, set some options and link the sources for the helper functions.

Remark: Depending on your R version the package osmplotr may be installed from github using devtools::install_github ("ropensci/osmplotr").

require(pacman) || install.packages("pacman")
## Loading required package: pacman
## [1] TRUE
pacman::p_load(coda, cowplot, demogR, dplyr, flexsurv, ggplot2, ggrepel, grid, 
               gridExtra, HMDHFDplus, kableExtra, Metrics, mortAAR, osmdata, 
               psych, readxl, reshape2, rjags, runjags, sf, tidyr, ggspatial)

options(scipen = 999)
options(dplyr.summarise.inform = FALSE)

source("./functions/gomp_MLE.R")
source("./functions/gomp_MLE_adapted.R")
source("./functions/gomp_MLE_interval.R")
source("./functions/gomp_anthr_age.R")
source("./functions/gomp_anthr_age_r.R")
source("./functions/gomp_known_age.R")
source("./functions/gomp_known_age_r.R")
source("./functions/helper_functions.R")
source("./functions/lt_MC.R")
source("./functions/lt_MC_Gomp.R")
RNGkind("L'Ecuyer-CMRG") # conservative random number generator to avoid periodicity

Important for saving time: Decide to run extensive code anew (app. 6 h +). In addition, you can set the folder for preprocessed files.

runCodeNew <- FALSE
#runCodeNew <- TRUE

# Ask for credentials of the Human Mortality Database if the code runs anew
if (runCodeNew){
  HMD_username <- readline(prompt = "Enter username: ")
  HMD_password <- readline(prompt="Enter password: ")
  credentials <- c(HMD_username, HMD_password)
}

# Specify filename prefix for saved files and create a folder if needed:
saveFileDir = "preprocessed_files"
if (saveFileDir %in% list.files(getwd())) {
  # Dir exists
}else{
  dir.create(file.path(".", saveFileDir), showWarnings = FALSE )
}
## NULL

Chapter 01 Introduction

Figure 1: Exemplary life table curves generated by Gompertz functions with different values for the \(\beta\) parameter.

# beta model values
beta1 <- 0.025
beta2 <- 0.04
beta3 <- 0.06
beta4 <- 0.09

# hgompertz(x, shape, rate): 
# x = age, shape = beta value, rate = derived from Sasaki & Kondo 2016 fig. 1, 2
# rate values according Sasaki & Kondo 2016 fig. 1, line 6, 30
Sab <- -2.624
Sbb <- 0.0393
Ma <- -7.119
Mb <- 0.0718
M1 <- Sab * (beta1 - Mb) / Sbb + Ma
M2 <- Sab * (beta2 - Mb) / Sbb + Ma
M3 <- Sab * (beta3 - Mb) / Sbb + Ma
M4 <- Sab * (beta4 - Mb) / Sbb + Ma

gridExtra::grid.arrange (
  
  ggplot()  + xlim(15, 100) + ylim(0, 0.4) +
    geom_function(fun = function(x) flexsurv::hgompertz(x - 15, 0.025, exp(M1)), 
                  aes(col = "\u03B2 = 0.025")) +
    geom_function(fun = function(x) flexsurv::hgompertz(x - 15, 0.04, exp(M2)),
                  aes(col = "\u03B2 = 0.04")) +
    geom_function(fun = function(x) flexsurv::hgompertz(x - 15, 0.06, exp(M3)), 
                  aes(col = "\u03B2 = 0.06")) +
    geom_function(fun = function(x) flexsurv::hgompertz(x - 15, 0.09, exp(M4)), 
                  aes(col = "\u03B2 = 0.9")) +
    ylab("hazard") + xlab("age in years") +
    theme_light() + 
    scale_colour_manual(values = c("red","blue","green", "dark grey")) +
    theme(legend.position = c(0.2, 0.7), legend.title = element_blank()),
  
  ggplot() + xlim(15, 105) +
    geom_function(fun = function(x) log(flexsurv::hgompertz(x - 15, 0.025, exp(M1))), colour = "red") +
    geom_function(fun = function(x) log(flexsurv::hgompertz(x - 15, 0.04, exp(M2))), colour= "blue") +
    geom_function(fun = function(x) log(flexsurv::hgompertz(x - 15, 0.06, exp(M3))), colour= "green") +
    geom_function(fun = function(x) log(flexsurv::hgompertz(x - 15, 0.09, exp(M4))), colour= "dark grey") +
    xlab("age in years") + ylab("hazard (log scale)") +
    theme_light(),
  
  ggplot() + xlim(15, 105) +
    geom_function(fun = function(x) flexsurv::dgompertz(x - 15, 0.025, exp(M1)), colour = "red") +
    geom_function(fun = function(x) flexsurv::dgompertz(x - 15, 0.04, exp(M2)), colour= "blue") +
    geom_function(fun = function(x) flexsurv::dgompertz(x - 15, 0.06, exp(M3)), colour= "green") +
    geom_function(fun = function(x) flexsurv::dgompertz(x - 15, 0.09, exp(M4)), colour= "dark grey") +
    xlab("age in years")  + ylab("density") +
    theme_light(),

  # gomp_lx() s. functions\helper_functions.R  
  ggplot() + xlim(15, 105) + ylim(0, 1) +
    geom_function(fun = function(x) gomp_lx(x - 15, exp(M1), 0.025), colour = "red") +
    geom_function(fun = function(x) gomp_lx(x - 15, exp(M2), 0.04), colour = "blue") +
    geom_function(fun = function(x) gomp_lx(x - 15, exp(M3), 0.06), colour = "green") +
    geom_function(fun = function(x) gomp_lx(x - 15, exp(M4), 0.09), colour = "dark grey") +
    ylab("survival") + xlab("age in years") +
    theme_light(),
  
  ncol = 2
) -> gompertz_plot

# Save the finished map object
ggsave(
  filename = "fig01_gompertz_plot.pdf",
  width = 8, height = 6,
  plot = gompertz_plot, 
  device = cairo_pdf,
  path = "documented"
)

Chapter 02 Materials and methods

Figure 3: Hazard curve (mx) for HMD UK data of the year 1841.

# Login needed to retrieve data from the Human Mortality Database
# https://mortality.org/

if (runCodeNew){
  login <- askYesNo(paste("Login for Human Mortality Database needed.",
                          "Do you want to proceed?", sep = "\n"),
                    default = FALSE)
  # get dx
  if (login){
    HMD_UK_result_1_year <- HMDHFDplus::readHMDweb("GBRTENW", "bltper_1x1", 
                                                   credentials[1], 
                                                   credentials[2])
    
    # saves results in Rda-object
    save(HMD_UK_result_1_year, file = file.path(".", saveFileDir, "HMD_UK_result_1_year.Rda") )
  }
} else {load(file.path(".", saveFileDir, "HMD_UK_result_1_year.Rda") )
  }


gridExtra::grid.arrange(
  ggplot(HMD_UK_result_1_year[which(HMD_UK_result_1_year$Year == 1841),]) + 
    geom_line(aes(x = Age, y = mx)) +
    scale_y_continuous(trans='log10') + labs(y = expression(m[x] * " (log scale)")) +
    annotate("rect", xmin = 7, xmax = 17, ymin = 0.004, ymax = 0.01, 
             alpha = .1,fill = "blue") +
    annotate (geom = "text", x = 12, y = 0.012, label = "zoom") +
    theme_light(),
  ggplot(HMD_UK_result_1_year[which(HMD_UK_result_1_year$Year == 1841),], 
         aes(x = Age, y = mx)) + scale_x_continuous(breaks=seq(8,16,2), limits=c(7, 17))  + 
    geom_line() + geom_point() +
    ylim(0.004, 0.01) +
    labs(y = expression(m[x]))+
    annotate (geom = "text", x = 10, y = 0.009, label = "zoomed in") +
    geom_segment(aes(x = 12, y = 0.007, xend = 12, yend = 0.0055),
                 arrow = arrow(length = unit(0.25, "cm")), colour = "red") +
    theme_light(),
  ncol = 1
) -> HMD_UK_hazard_plot

# Save the finished map object
ggsave(
  filename = "fig03_HMD_UK_hazard_plot.pdf",
  plot = HMD_UK_hazard_plot, 
  device = "pdf",
  path = "documented"
)
## Saving 7 x 5 in image

Chapter 03 Data

Figure 4: Major cemeteries in Greater London 1100–1850 used in the present study.

# Get the coordinates of sites to be plotted
sites_data <- rbind.data.frame(
    c("1","Bermondsey Abbey", 51.4975,-0.080833),
    c("2", "St Mary Spital", 51.518716, -0.079161),
    c("3","St Mary Graces",51.509289,-0.072916 ),
    c("4", "New Churchyard", 51.517403, -0.084216),
    c("5","St Benet Sherehog",51.513194,-0.091389),
    c("6", "Chelsea Old Church", 51.483222, -0.170795),
    c("7","St Bride's crypt",51.513802,-0.105292),
    c("8", "St Bride's lower churchyard", 51.515253, -0.104973),
    c("9", "Sheen's burial ground", 51.51480, -0.06760),
    c("10","St Marylebone", 51.5225,-0.152222),
    c("11",paste("St Marylebone's Paddington", "Street north", sep="\n"), 51.520869, -0.154515),
    c("12", "Bow Baptist church", 51.529540, -0.01580),
    c("13", "St Mary and St Michael", 51.51330, -0.05190)
  ) 
colnames(sites_data) <-c("nr", "name", "lat", "lon")
sites_data$lat<-as.numeric(sites_data$lat)
sites_data$lon<-as.numeric(sites_data$lon)

dat_sites <- st_as_sf(sites_data, 
                      coords = c("lon", "lat"), 
                      crs = 4326)

# Build a bounding box by the coordinates + 10% of the extent as frame
bbox <- matrix(
  c(
    min(sites_data$lon) - (0.1*(max(sites_data$lon)- min(sites_data$lon))),
    min(sites_data$lat) - (0.1*(max(sites_data$lat)- min(sites_data$lat))),
    max(sites_data$lon) + (0.1*(max(sites_data$lon)- min(sites_data$lon))),
    max(sites_data$lat) + (0.1*(max(sites_data$lat)- min(sites_data$lat)))
  ), 
  byrow = FALSE, nrow = 2, ncol = 2,
  dimnames = list(c('x','y'),c('min','max'))
)

# Querry the osm data
# If the bbox has been changed please run the statement to get the new osm data.

if (!exists ("q_admin8") | (runCodeNew == TRUE)) {
  q_admin8 <- bbox %>% opq() %>% 
    add_osm_feature(key = "boundary", value = "administrative") %>%
    add_osm_feature(key = "admin_level", value = "8") %>%
    osmdata_sf()
  }    

# Build the map
London_map <- ggplot() +
  geom_sf(data = q_admin8$osm_multipolygons, fill=rgb(0.9,0.9,0.9)) +
  geom_sf_text(data = q_admin8$osm_multipolygons, aes(label=sub('.*of ','',name)), size=3) +
  geom_sf(data = dat_sites,aes(), shape = 16, colour = "black", size = 2) +
  ggrepel::geom_label_repel(data = dat_sites, aes(label = nr, geometry = geometry),
  stat = "sf_coordinates", min.segment.length = 0, size=4) +
  annotate("label", x = -0.28, y = 51.38, hjust = 0, vjust = 0, size = 3,
                    label = paste(apply(sites_data[1:6,1:2],1,paste,collapse = ": "), 
                         collapse = "\n")) +
  annotate("label", x = -0.12, y = 51.38, hjust = 0, vjust = 0, size = 3,
           label = paste(apply(sites_data[7:13,1:2],1,paste,collapse = ": "), 
                         collapse = "\n")) +
  xlim (-0.28, 0.03) +
  ylim (51.38,51.58) +
  theme_light() +
  theme(panel.grid = element_blank()) +
  theme(axis.title = element_blank()) +
  ggspatial::annotation_scale(location = 'tl', height= unit(0.15, "cm"))
plot(London_map)

# Save the finished map object
ggsave(
  filename = "fig04_london_map.pdf",
  plot = London_map, 
  device = "pdf",
  path = "documented"
)
## Saving 7 x 5 in image

Table 1: Major cemeteries of London, without and with (r) compensation of population growth. beta – Gompertz beta parameter; M – modal age; ex20 – life expectancy at age 20; ex25 – life expectancy at age 25. Ranges computed with credible HDIs of 95%.

read.table("chapter_03_data/london_cemeteries.txt", header = T, sep = "\t") %>%
  knitr::kable(., col.names = c("Map no.",  "Name", "Period",   "Excavation year",  "Social character", "Absolute n",   "n analysed",   "n >= 12 years",    "References")) %>%
  kableExtra::kable_styling(latex_options = "HOLD_position") %>% unclass() %>% cat()
Map no. Name Period Excavation year Social character Absolute n n analysed n >= 12 years References
1 Bermondsey Abbey 1089–1538 1984–1995 monks 208 201 201 Dyson, Samuel, Steele, & Wright (2011)
2 St Mary Spital 1120–1538 1991–2007 commoners 10,516 5,387 Connell, Gray Jones, Redfern, & Walker (2012)
NA period 14: 1120–1200 347 329
NA period 15: 1200–1250 510 470
NA period 16: 1250–1400 1,392 1,361
NA period 17: 1400–1539 526 467
3 St Mary Graces 1350–1540 1986–1988 commoners 378 298 Grainger & Phillpotts (2011)
4 New Churchyard 1569–1739 2011–2015 low status 3,354 682 (category A) 556 Hartle, Carty, Henderson, Knox, & Walker (2017)
5 St Benet Sherehog 1670–1740 1994–1996 higher status 230 179 Miles, White, & Tankard (2008)
6 Chelsea Old church 1712–1842 2000 mixed 198 168 Cowie, Bekvalac, & Kausmally (2008)
7 St Brides crypt 1740–1853 high 216 J. L. Scheuer (1995); L. Scheuer (1998)
8 St Brides lower churchyard 1770–1849 low 606 379 Kausmally (2008)
9 Sheens burial ground 1763–1853 2006–2007 low 265 254 172 Henderson, Miles, & Walker (2013)
10 St Marylebone 1767–1859 1992; 2003 high status 301 226 Miles, Powers, Wroe-Brown, & Walker (2008)
11 St Marylebone Paddington Street north 1772–1853 2012–2013 high status 385 291 232 Henderson, Walker, & Miles (2015)
12 Bow Baptist church 1816–1853 2006; 2008 villagers 440 416 231 Henderson et al. (2013)
13 St Mary and St Michaels burial ground 1843–1854 2004–2005 low, Irish immigrants 760 705 284 Henderson et al. (2013)

Figure 5: Population development of London, compiled from Finlay & Shearer (1986), 39 table 1; Landers (1993), 41; 179 table 5.7; Weinreb, Hibbert, Keay, & Keay (2008), 655–657.

source("./chapter_03_data/London_population.R")
grid::grid.newpage()
grid::grid.draw(rbind(london_pop1, london_pop2))

Footnote 6: Re-calculation of population increase rates of London from Razzell & Spence (2007).

Calculated in ./chapter_03_data/London_population.R

knitr::kable(razz_df)%>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
date population rate.per.year
1520 55000 NA
1600 200000 0.016
1650 400000 0.014
1700 575000 0.007
1750 675000 0.003
1801 960000 0.007
1851 2685000 0.021

Chapter 04 Results

Preprocessing of data used in figure 6: Estimated modal ages.

Written sources

Basic statistics

The data is referenced and aggregated in “./chapter_04_results/historical_lifetables.R”. In this file, all records from individual preprocessing files located in “./liftables_preprocessed/” are sourced. The corresponding data files are stored in “./data/”.

London_1728_1840.R, Mortality_bills_1728_1840.txt, Source: Roberts & Cox (2003), 304 Table 6.5; > 100 years and < 1 year collapsed

source("./chapter_04_results/historical_lifetables.R")
kable(london_1728_1840_ranges, 
      caption = "London Mortality bills 1728-1840.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
London Mortality bills 1728-1840.
parameter ranges
beta 0.0324-0.0419
M 43.4-54.8 
kable(london_1728_1840_ranges_r, 
      caption = "London Mortality bills 1728-1840, corrected for population growth.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
London Mortality bills 1728-1840, corrected for population growth.
parameter ranges
beta_r 0.0327-0.0501
M_r 45.1-64.4
r 0.002-0.019

London_1841_raw_all.R, London_1841_raw.txt, Source: Graham (1842), 19 table q.

kable(London_1841_ranges, 
      caption = "Census data for London from 1841.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Census data for London from 1841.
parameter modes HDI.ranges
beta 0.0547 0.0510-0.0585
M 60.4164 58.9-61.7

English_Mortality.R, wrigley_et_al_1997_england_1640-1809.txt, Source: Wrigley, Oeppen, Davies, & Schofield (1997), 290 table 6.19

kable(eng_mort_ranges, 
      caption = "English mortality data.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
English mortality data.
parameter ranges
beta 0.0438-0.0608
M 52.2-67.4

HMD_UK_ranges.R

The data from the Human Mortality Database (https://mortality.org/) were retrieved with a personal account using the R package HMDHFDplus. Therefore, we only provide the processed data here.

kable(HMD_UK_ranges, caption = "Human Mortality Database UK.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Human Mortality Database UK.
parameter ranges
beta 0.05-0.0654
M 64.2-70.2

English_Peers.R, russell.txt, Source: La Poutré & Janssen (2021), table 2

kable(peers_ranges, caption = "English Peers") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
English Peers
parameter modes HDI.ranges
beta 0.0613 0.0559-0.0660
M 58.1758 56.4-59.8
e20 33.4148 NA
e25 29.4926 NA

Medieval_England.R, Christ_church_monks.txt, Source: Hatcher, Piper, & Stone (2006), 28 table 2

kable(monks_ranges, caption = "Christ Church monks") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
Christ Church monks
parameter modes HDI.ranges
beta 0.0461 0.0398-0.0523
M 52.7659 48.9-56.0
e20 31.0948 NA
e25 27.7530 NA

Extented statistics

kable(london_1728_1840_result, 
      caption = "London Mortality bills 1728-1840.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London Mortality bills 1728-1840.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1728 alpha 1.000108 1.000395 0.0146970 0.0146465 0.0145984 16365.6 0.0000105 0.95 0.0121552 0.0173894
X1728 beta 1.000120 1.000451 0.0349080 0.0349052 0.0347825 16828.8 0.0000207 0.95 0.0296327 0.0401025
X1728 M 1.000140 1.000453 44.6140062 44.8625026 45.0618057 16114.3 0.0233898 0.95 38.7086866 50.1735217
X1730 alpha 1.000025 1.000130 0.0156646 0.0156056 0.0154789 18337.2 0.0000111 0.95 0.0127633 0.0186414
X1730 beta 1.000039 1.000168 0.0325426 0.0325361 0.0324144 18117.0 0.0000207 0.95 0.0270931 0.0379764
X1730 M 1.000030 1.000142 42.2093093 42.5573739 43.4233691 18020.2 0.0277785 0.95 34.7516415 49.0050848
X1740 alpha 1.000112 1.000403 0.0153878 0.0153418 0.0152749 17990.7 0.0000100 0.95 0.0128087 0.0180175
X1740 beta 1.000101 1.000385 0.0337646 0.0337606 0.0335736 17926.6 0.0000190 0.95 0.0288006 0.0387511
X1740 M 1.000157 1.000484 43.0932517 43.3416150 44.0450446 17518.4 0.0233112 0.95 36.9618783 48.8486639
X1750 alpha 1.000308 1.001170 0.0151942 0.0151449 0.0150989 18259.5 0.0000101 0.95 0.0125952 0.0179004
X1750 beta 1.000351 1.001292 0.0342717 0.0342730 0.0342242 18121.9 0.0000195 0.95 0.0290667 0.0393662
X1750 M 1.000317 1.001174 43.5548106 43.8136623 44.5458564 17813.4 0.0230371 0.95 37.3772875 49.2243556
X1760 alpha 1.000338 1.000801 0.0145711 0.0145269 0.0143509 17449.6 0.0000100 0.95 0.0120404 0.0171711
X1760 beta 1.000241 1.000520 0.0350287 0.0350196 0.0349168 17085.2 0.0000201 0.95 0.0299236 0.0402371
X1760 M 1.000363 1.000866 44.8827829 45.1095653 45.6086874 17106.4 0.0221726 0.95 39.1055721 50.2653901
X1770 alpha 1.000175 1.000588 0.0143221 0.0142774 0.0142718 17407.1 0.0000099 0.95 0.0117796 0.0169045
X1770 beta 1.000110 1.000381 0.0355969 0.0356004 0.0358743 17291.4 0.0000203 0.95 0.0304311 0.0408902
X1770 M 1.000178 1.000591 45.4300281 45.6462299 45.7955369 17214.1 0.0214852 0.95 39.8417826 50.7260430
X1780 alpha 1.000269 1.000935 0.0136238 0.0135783 0.0135358 16804.1 0.0000095 0.95 0.0112248 0.0160214
X1780 beta 1.000239 1.000906 0.0367220 0.0367253 0.0367228 16729.5 0.0000201 0.95 0.0317062 0.0419311
X1780 M 1.000314 1.001006 46.8874156 47.0760558 47.5932925 16847.5 0.0195467 0.95 41.7873949 51.6004245
X1790 alpha 1.000213 1.000318 0.0126517 0.0126141 0.0126627 16987.5 0.0000089 0.95 0.0103904 0.0149291
X1790 beta 1.000153 1.000189 0.0385170 0.0385078 0.0385633 16735.7 0.0000203 0.95 0.0333069 0.0435894
X1790 M 1.000247 1.000390 48.8232330 48.9686652 49.3336238 17313.3 0.0172234 0.95 44.3303384 53.1112910
X1800 alpha 1.000066 1.000135 0.0116898 0.0116448 0.0115679 15913.4 0.0000085 0.95 0.0096159 0.0138219
X1800 beta 1.000108 1.000229 0.0399437 0.0399437 0.0398114 16280.5 0.0000202 0.95 0.0348971 0.0449998
X1800 M 1.000048 1.000103 50.7070955 50.8409969 51.0720614 16902.5 0.0156219 0.95 46.6498010 54.5415198
X1810 alpha 1.000554 1.001977 0.0115040 0.0114672 0.0113409 15693.3 0.0000082 0.95 0.0095496 0.0135586
X1810 beta 1.000705 1.002539 0.0384284 0.0384204 0.0384387 15514.8 0.0000196 0.95 0.0336019 0.0431446
X1810 M 1.000514 1.001824 51.3269015 51.4533360 51.7564282 16513.8 0.0160886 0.95 47.1307998 55.1816194
X1820 alpha 1.000033 1.000085 0.0104903 0.0104573 0.0103834 15105.4 0.0000079 0.95 0.0086455 0.0124121
X1820 beta 1.000043 1.000117 0.0403661 0.0403518 0.0400258 14941.4 0.0000204 0.95 0.0354922 0.0452322
X1820 M 1.000026 1.000068 53.3477816 53.4500376 53.7200147 16242.5 0.0145904 0.95 49.6159817 56.8461806
X1830 alpha 1.000262 1.000742 0.0098565 0.0098250 0.0097444 14287.5 0.0000077 0.95 0.0080915 0.0116937
X1830 beta 1.000328 1.000824 0.0420331 0.0420192 0.0419423 14811.9 0.0000207 0.95 0.0371686 0.0470269
X1830 M 1.000204 1.000597 54.4845443 54.5690888 54.8316675 16013.8 0.0134579 0.95 51.1240793 57.7697242
X1840 alpha 1.000065 1.000175 0.0103000 0.0102638 0.0101621 14542.4 0.0000080 0.95 0.0084719 0.0122192
X1840 beta 1.000062 1.000189 0.0409226 0.0409164 0.0407728 14161.3 0.0000212 0.95 0.0360077 0.0458839
X1840 M 1.000053 1.000143 53.6798657 53.7773975 53.7555529 15909.8 0.0144310 0.95 50.0411401 57.1294679 
kable(london_1728_1840_result_r, 
      caption = "London Mortality bills 1728-1840, corrected for population growth.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London Mortality bills 1728-1840, corrected for population growth.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1728 alpha 1.000493 1.001271 0.0120388 0.0119639 0.0117705 13219.2 0.0000127 0.95 0.0092381 0.0149068
X1728 beta 1.000293 1.000781 0.0373256 0.0373497 0.0374499 14626.6 0.0000261 0.95 0.0312018 0.0435282
X1728 M 1.000607 1.001494 50.2038587 50.4495217 50.9806000 13687.7 0.0264982 0.95 43.9280763 55.9188957
X1728 rate 1.000147 1.000459 0.0066686 0.0066694 0.0067571 27227.8 0.0000151 0.95 0.0018302 0.0116186
X1730 alpha 1.000269 1.000770 0.0148858 0.0147951 0.0145680 14694.8 0.0000148 0.95 0.0115075 0.0185145
X1730 beta 1.000150 1.000455 0.0324320 0.0324651 0.0327068 16554.5 0.0000253 0.95 0.0260065 0.0387515
X1730 M 1.000349 1.000914 43.6813384 44.1622266 45.0521696 14720.2 0.0375115 0.95 34.6717649 52.0836240
X1730 rate 1.000125 1.000492 0.0017597 0.0017647 0.0017560 31387.5 0.0000140 0.95 -0.0031019 0.0066355
X1740 alpha 1.000329 1.000720 0.0146610 0.0145783 0.0142673 12838.5 0.0000145 0.95 0.0115556 0.0179785
X1740 beta 1.000371 1.001036 0.0338783 0.0339015 0.0340453 14559.4 0.0000244 0.95 0.0281672 0.0397172
X1740 M 1.000313 1.000633 44.5110399 44.8625313 45.6855802 12927.7 0.0334910 0.95 36.8686339 51.5460098
X1740 rate 1.000079 1.000225 0.0015451 0.0015464 0.0015893 25927.1 0.0000155 0.95 -0.0033455 0.0064169
X1750 alpha 1.000091 1.000301 0.0126650 0.0125920 0.0124096 13381.2 0.0000131 0.95 0.0097778 0.0156841
X1750 beta 1.000158 1.000520 0.0363874 0.0364000 0.0364127 15055.2 0.0000254 0.95 0.0303579 0.0425971
X1750 M 1.000109 1.000338 48.8679712 49.1288156 49.6582623 13657.6 0.0280568 0.95 42.3123463 55.0499366
X1750 rate 1.000002 1.000003 0.0061501 0.0061570 0.0061586 28511.9 0.0000148 0.95 0.0012302 0.0110002
X1760 alpha 1.000046 1.000138 0.0118787 0.0118090 0.0117666 13167.5 0.0000125 0.95 0.0091035 0.0146849
X1760 beta 1.000017 1.000101 0.0375028 0.0375223 0.0376118 15087.9 0.0000254 0.95 0.0314240 0.0436194
X1760 M 1.000075 1.000168 50.5533524 50.7836185 51.6251396 13738.2 0.0259954 0.95 44.4208165 56.2002552
X1760 rate 1.000014 1.000079 0.0068523 0.0068519 0.0068244 26661.9 0.0000153 0.95 0.0019504 0.0117469
X1770 alpha 1.000380 1.001203 0.0121911 0.0121201 0.0120472 13162.6 0.0000128 0.95 0.0093360 0.0150793
X1770 beta 1.000576 1.001801 0.0375407 0.0375624 0.0378417 14253.2 0.0000262 0.95 0.0314411 0.0437422
X1770 M 1.000298 1.000964 49.8528284 50.0817560 50.3580496 13551.1 0.0264695 0.95 43.7540998 55.7240017
X1770 rate 1.000094 1.000275 0.0053016 0.0052956 0.0052041 27499.5 0.0000151 0.95 0.0004322 0.0101881
X1780 alpha 1.001089 1.003872 0.0100912 0.0100242 0.0098793 13153.1 0.0000107 0.95 0.0077807 0.0125681
X1780 beta 1.000765 1.002770 0.0407636 0.0407668 0.0406275 14796.3 0.0000251 0.95 0.0347108 0.0466753
X1780 M 1.001100 1.003857 54.2249121 54.3794171 54.9416590 14389.5 0.0204589 0.95 49.2715760 58.8762349
X1780 rate 1.000574 1.002146 0.0098681 0.0098605 0.0099363 27001.6 0.0000152 0.95 0.0049838 0.0147621
X1790 alpha 1.001213 1.004101 0.0075877 0.0075309 0.0073853 13394.6 0.0000085 0.95 0.0057156 0.0095457
X1790 beta 1.000912 1.003290 0.0458236 0.0458462 0.0458421 14781.8 0.0000260 0.95 0.0396890 0.0520899
X1790 M 1.001011 1.003327 59.2913458 59.3690803 59.3913393 16477.9 0.0152745 0.95 55.4175368 63.1058941
X1790 rate 1.000444 1.001551 0.0163690 0.0163788 0.0165687 24985.7 0.0000158 0.95 0.0115298 0.0213122
X1800 alpha 1.000387 1.001251 0.0067681 0.0067205 0.0066553 12952.0 0.0000077 0.95 0.0050763 0.0085024
X1800 beta 1.000332 1.001184 0.0477523 0.0477522 0.0478150 14065.9 0.0000260 0.95 0.0416756 0.0537888
X1800 M 1.000285 1.000812 60.9817744 61.0368872 61.0870784 17235.5 0.0136042 0.95 57.4198438 64.4259602
X1800 rate 1.000109 1.000405 0.0172752 0.0172792 0.0173804 24208.7 0.0000160 0.95 0.0123856 0.0221662
X1810 alpha 1.000202 1.000668 0.0062540 0.0062051 0.0060517 12219.0 0.0000076 0.95 0.0046618 0.0079061
X1810 beta 1.000300 1.000974 0.0466685 0.0466843 0.0466222 13819.9 0.0000264 0.95 0.0405736 0.0527045
X1810 M 1.000099 1.000312 63.1437477 63.1965586 63.1840070 16815.0 0.0141963 0.95 59.5131108 66.7201334
X1810 rate 1.000063 1.000170 0.0186911 0.0186887 0.0186977 21565.1 0.0000171 0.95 0.0138016 0.0236117
X1820 alpha 1.000215 1.000279 0.0057095 0.0056649 0.0055172 11737.7 0.0000072 0.95 0.0042407 0.0072573
X1820 beta 1.000270 1.000463 0.0488446 0.0488583 0.0489581 12730.0 0.0000279 0.95 0.0425629 0.0548806
X1820 M 1.000058 1.000058 64.0351053 64.0783090 64.1736064 17185.5 0.0129582 0.95 60.6476942 67.3084873
X1820 rate 1.000055 1.000145 0.0183072 0.0183033 0.0183194 21399.3 0.0000171 0.95 0.0134475 0.0232238
X1830 alpha 1.000851 1.002718 0.0056217 0.0055807 0.0055025 11196.7 0.0000071 0.95 0.0041951 0.0071180
X1830 beta 1.000811 1.002726 0.0500179 0.0500137 0.0501418 12016.8 0.0000281 0.95 0.0440217 0.0561384
X1830 M 1.000547 1.001650 63.7874764 63.8285439 63.9588124 16675.9 0.0124725 0.95 60.5930623 66.9110171
X1830 rate 1.000415 1.001353 0.0169139 0.0169158 0.0170653 21735.5 0.0000169 0.95 0.0119901 0.0217235
X1840 alpha 1.001912 1.006772 0.0055618 0.0055194 0.0053917 11400.5 0.0000071 0.95 0.0040979 0.0070495
X1840 beta 1.001683 1.006126 0.0496698 0.0496734 0.0495466 12494.4 0.0000281 0.95 0.0435270 0.0558486
X1840 M 1.001165 1.004232 64.1728612 64.2122002 64.4409872 16778.0 0.0127460 0.95 60.9228836 67.4118054
X1840 rate 1.000770 1.002796 0.0184375 0.0184351 0.0184647 20471.4 0.0000175 0.95 0.0135561 0.0233655 
kable(London_1841_result, 
      caption = "Census data for London from 1841.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Census data for London from 1841.
PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
a 1.000227 1.000481 0.0045780 0.0045654 0.0045126 15366.4 0.0000030 0.95 0.0038745 0.0053284
b 1.000173 1.000361 0.0547652 0.0547581 0.0546507 15261.7 0.0000155 0.95 0.0510256 0.0585294
M 1.000098 1.000288 60.3512664 60.3640713 60.4164328 26323.3 0.0044223 0.95 58.9378882 61.7484732 
kable(eng_mort_result, caption = "English mortality data.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
English mortality data.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1640 alpha 1.000116 1.000213 0.0109640 0.0109440 0.0108724 20086.8 0.0000055 0.95 0.0094508 0.0125183
X1640 beta 1.000128 1.000269 0.0473794 0.0473646 0.0471615 19457.0 0.0000160 0.95 0.0430271 0.0517521
X1640 M 1.000098 1.000168 55.8790864 55.9257645 56.0762781 22766.9 0.0074788 0.95 53.6542245 58.0607633
X1650 alpha 1.000196 1.000699 0.0086495 0.0086305 0.0086386 17477.0 0.0000050 0.95 0.0073694 0.0099516
X1650 beta 1.000238 1.000818 0.0534298 0.0534191 0.0532174 17097.8 0.0000176 0.95 0.0488730 0.0579356
X1650 M 1.000122 1.000456 59.0892102 59.1180884 59.1222939 22875.6 0.0058105 0.95 57.3707403 60.8059797
X1660 alpha 1.000538 1.001899 0.0091323 0.0091133 0.0090836 17736.5 0.0000051 0.95 0.0078190 0.0104985
X1660 beta 1.000442 1.001588 0.0507107 0.0507012 0.0506517 17263.0 0.0000172 0.95 0.0463039 0.0551739
X1660 M 1.000484 1.001711 58.8100849 58.8427992 58.8427140 22595.3 0.0063824 0.95 56.9061034 60.6611103
X1670 alpha 1.000280 1.000678 0.0109726 0.0109471 0.0109033 20090.3 0.0000056 0.95 0.0094600 0.0125515
X1670 beta 1.000338 1.000812 0.0444972 0.0445019 0.0446316 19399.7 0.0000157 0.95 0.0402542 0.0488448
X1670 M 1.000211 1.000529 56.4443366 56.5061422 56.5992418 22544.4 0.0083487 0.95 53.9239107 58.8183187
X1680 alpha 1.000560 1.001531 0.0134499 0.0134251 0.0133309 22339.5 0.0000061 0.95 0.0116869 0.0152420
X1680 beta 1.000479 1.001399 0.0435646 0.0435605 0.0437501 21337.1 0.0000151 0.95 0.0392159 0.0478531
X1680 M 1.000597 1.001611 51.9412993 52.0117614 52.1884363 23152.8 0.0091727 0.95 49.1667363 54.6014009
X1690 alpha 1.000203 1.000424 0.0100036 0.0099815 0.0099278 19068.4 0.0000053 0.95 0.0085828 0.0114492
X1690 beta 1.000217 1.000487 0.0457255 0.0457144 0.0457837 18458.1 0.0000160 0.95 0.0414631 0.0499716
X1690 M 1.000156 1.000323 58.2265512 58.2748183 58.3311613 22552.3 0.0076819 0.95 55.9044003 60.4191960
X1700 alpha 1.000247 1.000813 0.0097904 0.0097696 0.0097670 19048.9 0.0000052 0.95 0.0083976 0.0112137
X1700 beta 1.000228 1.000792 0.0469162 0.0469091 0.0468449 18524.9 0.0000160 0.95 0.0426635 0.0512282
X1700 M 1.000210 1.000697 58.3940436 58.4388608 58.4010030 22362.5 0.0073779 0.95 56.2165699 60.5292073
X1710 alpha 1.000629 1.002202 0.0076344 0.0076175 0.0075883 16583.9 0.0000046 0.95 0.0064833 0.0088178
X1710 beta 1.000810 1.002798 0.0547320 0.0547184 0.0547561 16149.3 0.0000181 0.95 0.0502213 0.0592441
X1710 M 1.000354 1.001230 61.0059909 61.0278089 61.0396872 23904.2 0.0053119 0.95 59.3643989 62.5807876
X1720 alpha 1.000438 1.001584 0.0080028 0.0079824 0.0079301 17173.5 0.0000047 0.95 0.0068173 0.0092105
X1720 beta 1.000453 1.001645 0.0560063 0.0560001 0.0558861 16622.0 0.0000179 0.95 0.0514205 0.0604697
X1720 M 1.000297 1.001094 59.7548666 59.7785061 59.8227855 23615.5 0.0051845 0.95 58.1648789 61.2877274
X1730 alpha 1.000128 1.000485 0.0067962 0.0067781 0.0067500 15125.2 0.0000045 0.95 0.0057413 0.0078882
X1730 beta 1.000132 1.000481 0.0561362 0.0561233 0.0561525 14537.5 0.0000193 0.95 0.0516431 0.0607418
X1730 M 1.000086 1.000325 62.6345173 62.6558894 62.6742840 23395.6 0.0050475 0.95 61.1122439 64.1406077
X1740 alpha 1.000185 1.000678 0.0067863 0.0067674 0.0067507 15383.6 0.0000045 0.95 0.0057019 0.0078702
X1740 beta 1.000260 1.000953 0.0566936 0.0566911 0.0568096 15043.4 0.0000191 0.95 0.0520709 0.0612724
X1740 M 1.000063 1.000245 62.4655115 62.4849711 62.4345863 22893.7 0.0051037 0.95 60.9419302 63.9688404
X1750 alpha 1.000389 1.001407 0.0053793 0.0053645 0.0053635 13451.8 0.0000040 0.95 0.0044682 0.0062959
X1750 beta 1.000443 1.001627 0.0595510 0.0595305 0.0594825 12966.5 0.0000210 0.95 0.0548610 0.0642515
X1750 M 1.000167 1.000607 65.4071998 65.4213962 65.4642394 24607.7 0.0044311 0.95 64.0354191 66.7582250
X1760 alpha 1.000180 1.000387 0.0080565 0.0080378 0.0079359 17802.8 0.0000047 0.95 0.0068516 0.0092887
X1760 beta 1.000187 1.000346 0.0488550 0.0488417 0.0488743 16840.4 0.0000169 0.95 0.0445037 0.0531121
X1760 M 1.000119 1.000328 61.9016665 61.9336352 62.0050035 23618.5 0.0063598 0.95 59.9327761 63.7618010
X1770 alpha 1.000469 1.001234 0.0067654 0.0067476 0.0066997 14881.8 0.0000045 0.95 0.0057073 0.0078687
X1770 beta 1.000501 1.001341 0.0538935 0.0538804 0.0536262 14373.8 0.0000192 0.95 0.0494452 0.0584665
X1770 M 1.000270 1.000709 63.5277738 63.5489910 63.4921572 22585.6 0.0054864 0.95 61.9173469 65.1383522
X1780 alpha 1.000347 1.001235 0.0066384 0.0066225 0.0066110 15713.1 0.0000043 0.95 0.0055976 0.0076907
X1780 beta 1.000349 1.001303 0.0570824 0.0570677 0.0571475 15127.7 0.0000188 0.95 0.0526292 0.0616896
X1780 M 1.000195 1.000710 62.7166530 62.7352113 62.7235429 24154.0 0.0048243 0.95 61.2201635 64.1540268
X1790 alpha 1.000180 1.000376 0.0058127 0.0057951 0.0057825 13899.0 0.0000042 0.95 0.0048677 0.0068164
X1790 beta 1.000229 1.000478 0.0580897 0.0580826 0.0579337 13447.1 0.0000206 0.95 0.0533856 0.0627649
X1790 M 1.000055 1.000174 64.6577738 64.6756380 64.7246120 23430.8 0.0047208 0.95 63.2361972 66.0657933
X1800 alpha 1.000697 1.002167 0.0046142 0.0045977 0.0045567 12391.5 0.0000037 0.95 0.0038253 0.0054317
X1800 beta 1.000709 1.002222 0.0608363 0.0608357 0.0608310 11940.3 0.0000219 0.95 0.0561091 0.0654678
X1800 M 1.000239 1.000822 67.4325112 67.4451148 67.4486965 26907.8 0.0039816 0.95 66.1359322 68.6958522 
kable(HMD_UK_result, caption = "Human Mortality Database UK.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Human Mortality Database UK.
year parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
X1841 alpha 1.000163 1.000417 0.0036316 0.0036148 0.0035704 13786.9 0.0000032 0.95 0.0029186 0.0043694
X1841 beta 1.000156 1.000468 0.0519888 0.0519880 0.0522191 13557.1 0.0000185 0.95 0.0476828 0.0561015
X1841 M 1.000083 1.000148 66.2542881 66.2748935 66.3111134 25227.7 0.0056085 0.95 64.4997322 67.9878895
X1845 alpha 1.000079 1.000297 0.0042938 0.0042780 0.0042669 14758.1 0.0000036 0.95 0.0034647 0.0051540
X1845 beta 1.000067 1.000247 0.0498996 0.0498859 0.0500069 14606.7 0.0000180 0.95 0.0455985 0.0541474
X1845 M 1.000065 1.000255 64.2120906 64.2353737 64.2258466 24443.1 0.0062539 0.95 62.2412879 66.0782225
X1850 alpha 1.000973 1.003549 0.0037558 0.0037391 0.0036783 13963.2 0.0000033 0.95 0.0030110 0.0045196
X1850 beta 1.000868 1.003159 0.0517607 0.0517548 0.0515669 13902.2 0.0000185 0.95 0.0475374 0.0561228
X1850 M 1.000670 1.002447 65.7445767 65.7656894 65.8470383 24788.4 0.0057544 0.95 63.9683713 67.5152044
X1855 alpha 1.000156 1.000325 0.0034310 0.0034165 0.0034148 13071.2 0.0000031 0.95 0.0027387 0.0041407
X1855 beta 1.000111 1.000252 0.0533405 0.0533264 0.0532089 12901.9 0.0000193 0.95 0.0489858 0.0575821
X1855 M 1.000055 1.000176 66.5070750 66.5214941 66.5377049 24496.9 0.0055156 0.95 64.7810996 68.1628553
X1860 alpha 1.000103 1.000169 0.0034785 0.0034615 0.0034062 13432.3 0.0000031 0.95 0.0027794 0.0041924
X1860 beta 1.000118 1.000200 0.0532621 0.0532640 0.0532106 13350.6 0.0000189 0.95 0.0490210 0.0575846
X1860 M 1.000016 1.000032 66.2956647 66.3134949 66.3500169 24949.1 0.0054798 0.95 64.5756127 67.9675086
X1865 alpha 1.000093 1.000333 0.0035991 0.0035837 0.0035330 13810.1 0.0000031 0.95 0.0028932 0.0043267
X1865 beta 1.000108 1.000353 0.0530530 0.0530491 0.0530859 13658.1 0.0000185 0.95 0.0488013 0.0572954
X1865 M 1.000045 1.000177 65.7780212 65.7953467 65.8802464 25507.4 0.0054316 0.95 64.0717897 67.4665740
X1870 alpha 1.000077 1.000191 0.0035027 0.0034908 0.0034765 13760.3 0.0000030 0.95 0.0028292 0.0042127
X1870 beta 1.000110 1.000242 0.0536849 0.0536587 0.0535650 13616.9 0.0000184 0.95 0.0495385 0.0579499
X1870 M 1.000013 1.000070 65.9071237 65.9205478 65.8577523 25746.8 0.0052524 0.95 64.2645935 67.5678728
X1875 alpha 1.000092 1.000343 0.0030605 0.0030478 0.0030211 12815.0 0.0000028 0.95 0.0024475 0.0036823
X1875 beta 1.000131 1.000471 0.0568401 0.0568279 0.0568980 12685.7 0.0000193 0.95 0.0526071 0.0611415
X1875 M 1.000031 1.000141 66.4668857 66.4785272 66.5086127 26537.0 0.0047162 0.95 64.9506366 67.9602202
X1880 alpha 1.000119 1.000291 0.0027376 0.0027242 0.0026867 12292.1 0.0000026 0.95 0.0021904 0.0033047
X1880 beta 1.000171 1.000388 0.0580794 0.0580802 0.0580583 12275.9 0.0000195 0.95 0.0538930 0.0623071
X1880 M 1.000016 1.000046 67.6639684 67.6752899 67.6594434 26763.5 0.0045057 0.95 66.2138218 69.0997903
X1885 alpha 1.000329 1.000699 0.0024297 0.0024169 0.0023954 11472.9 0.0000024 0.95 0.0019319 0.0029532
X1885 beta 1.000279 1.000617 0.0605593 0.0605577 0.0605172 11375.3 0.0000207 0.95 0.0561612 0.0648427
X1885 M 1.000124 1.000309 68.1749533 68.1842585 68.1928238 26834.9 0.0042250 0.95 66.8018933 69.5153058
X1890 alpha 1.000121 1.000451 0.0024118 0.0023997 0.0023802 11867.7 0.0000024 0.95 0.0019247 0.0029285
X1890 beta 1.000146 1.000531 0.0614665 0.0614588 0.0613662 11669.1 0.0000205 0.95 0.0571518 0.0657954
X1890 M 1.000045 1.000148 67.7519542 67.7613179 67.8037905 28081.6 0.0040695 0.95 66.4069818 69.0759956
X1895 alpha 1.000328 1.001210 0.0019825 0.0019735 0.0019634 10586.6 0.0000021 0.95 0.0015598 0.0024219
X1895 beta 1.000267 1.000994 0.0637922 0.0637712 0.0636859 10594.5 0.0000217 0.95 0.0594245 0.0681856
X1895 M 1.000224 1.000819 69.4924393 69.4994274 69.5249671 28489.7 0.0038280 0.95 68.2103261 70.7410684
X1900 alpha 1.000051 1.000194 0.0017882 0.0017794 0.0017686 10113.1 0.0000020 0.95 0.0013975 0.0021792
X1900 beta 1.000061 1.000247 0.0653147 0.0653019 0.0653664 10036.7 0.0000222 0.95 0.0609626 0.0696771
X1900 M 1.000007 1.000020 70.1656919 70.1713832 70.1615274 28126.0 0.0036879 0.95 68.9548389 71.3801825 
kable(peers_result, caption = "English Peers.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
English Peers.
PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
a 1.000356 1.001061 0.0044095 0.0043879 0.0043263 11315.3 0.0000044 0.95 0.0035238 0.0053575
b 1.000307 1.000854 0.0609452 0.0609518 0.0612976 11121.9 0.0000244 0.95 0.0559415 0.0660412
M 1.000196 1.000696 58.1500750 58.1648975 58.1757927 20660.4 0.0059675 0.95 56.4492001 59.8036275 
kable(monks_result, caption = "Christ Church monks.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
Christ Church monks.
start end parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
1395 1505 alpha 1.000569 1.001661 0.0102993 0.0102563 0.0100488 13991.9 0.0000096 0.95 0.0081076 0.0125497
1395 1505 beta 1.000498 1.001436 0.0459467 0.0459287 0.0461060 13623.6 0.0000273 0.95 0.0397953 0.0523389
1395 1505 M 1.000504 1.001504 52.5281106 52.6296486 52.7658924 15808.5 0.0143226 0.95 48.9344189 55.9631681

London cemeteries

The data is mainly hard coded in the file ./chapter_04_results/Wellcome_DB.R.

Only St. Bride’s crypt is excluded but available from the Museum of London upon request. For general information: https://www.museumoflondon.org.uk go for: Collections > Archaeology at the Museum of London > Wellcome Osteological Research Database > St. Bride’s Church Fleet Street. If runCodeNew == TRUE the file ./lifetables_processing/stbrides_crypt.R will ask for the location of the retrieved dataset (Excel sheet) and process the data. In any other case pre-processed data will be loaded.

source("./lifetables_processing/stbrides_crypt.R")
source("./chapter_04_results/Wellcome_DB.R")
kable(wellcome_result) %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
cemetery start end parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
Bermondsey Abbey 1089 1538 alpha 1.000095 1.000352 0.0119872 0.0118695 0.0117349 26882.4 0.0000115 0.95 0.0084108 0.0157410
Bermondsey Abbey 1089 1538 beta 1.000115 1.000319 0.0410531 0.0410516 0.0413654 23098.5 0.0000312 0.95 0.0318561 0.0503895
Bermondsey Abbey 1089 1538 M 1.000071 1.000266 41.8366810 42.1437778 42.5664355 29309.6 0.0207896 0.95 34.6719658 48.4310632
St. Mary Graces 1350 1540 alpha 1.000196 1.000732 0.0197808 0.0196850 0.0195223 35662.0 0.0000118 0.95 0.0154857 0.0241619
St. Mary Graces 1350 1540 beta 1.000244 1.000894 0.0346722 0.0346636 0.0349129 29450.8 0.0000239 0.95 0.0266567 0.0427213
St. Mary Graces 1350 1540 M 1.000288 1.000951 27.6620555 28.2853721 29.0829030 31343.0 0.0275212 0.95 17.7908628 36.1544161
St. Mary Hospital, 1120-1200 1120 1200 alpha 1.000021 1.000058 0.0249328 0.0248411 0.0247596 47240.6 0.0000108 0.95 0.0203838 0.0295337
St. Mary Hospital, 1120-1200 1120 1200 beta 1.000010 1.000041 0.0363031 0.0363142 0.0366087 42155.0 0.0000184 0.95 0.0288655 0.0437148
St. Mary Hospital, 1120-1200 1120 1200 M 1.000014 1.000048 21.9000883 22.4278307 23.6171674 41316.5 0.0217592 0.95 12.9358328 29.6933479
St. Mary Hospital, 1200-1250 1200 1250 alpha 1.000142 1.000479 0.0299501 0.0298832 0.0296347 50227.8 0.0000103 0.95 0.0254561 0.0345077
St. Mary Hospital, 1200-1250 1200 1250 beta 1.000145 1.000390 0.0356927 0.0356959 0.0355017 44544.0 0.0000163 0.95 0.0288836 0.0423855
St. Mary Hospital, 1200-1250 1200 1250 M 1.000138 1.000388 16.4726206 16.9685941 17.8228768 43773.7 0.0209091 0.95 7.6941741 24.3391668
St. Mary Hospital, 1250-1400 1250 1400 alpha 1.000058 1.000230 0.0183232 0.0182986 0.0182568 30711.1 0.0000060 0.95 0.0162397 0.0203837
St. Mary Hospital, 1250-1400 1250 1400 beta 1.000039 1.000160 0.0580756 0.0580643 0.0577145 27569.9 0.0000162 0.95 0.0529190 0.0634424
St. Mary Hospital, 1250-1400 1250 1400 M 1.000056 1.000226 31.8403051 31.8802975 31.9815271 32452.4 0.0050096 0.95 30.0460798 33.5688087
St. Mary Hospital, 1400-1539 1400 1539 alpha 1.000184 1.000413 0.0262455 0.0261845 0.0258468 45106.6 0.0000098 0.95 0.0222297 0.0303974
St. Mary Hospital, 1400-1539 1400 1539 beta 1.000202 1.000384 0.0374668 0.0374646 0.0373648 37992.2 0.0000178 0.95 0.0307176 0.0443176
St. Mary Hospital, 1400-1539 1400 1539 M 1.000255 1.000509 21.1562579 21.5422484 22.2118499 38394.6 0.0188420 0.95 13.7317283 27.8355824
New Churchyard 1569 1739 alpha 1.000100 1.000375 0.0257447 0.0256826 0.0256229 40693.9 0.0000097 0.95 0.0219664 0.0296497
New Churchyard 1569 1739 beta 1.000143 1.000447 0.0365472 0.0365523 0.0364771 33659.4 0.0000185 0.95 0.0298776 0.0431955
New Churchyard 1569 1739 M 1.000167 1.000489 21.2258180 21.6422371 22.4873708 34065.6 0.0202506 0.95 13.6829257 27.9012158
St. Benet Sherehog 1670 1740 alpha 1.000103 1.000388 0.0159324 0.0158024 0.0157241 35332.7 0.0000126 0.95 0.0114989 0.0206750
St. Benet Sherehog 1670 1740 beta 1.000166 1.000541 0.0354819 0.0354675 0.0352938 29914.9 0.0000268 0.95 0.0265131 0.0446216
St. Benet Sherehog 1670 1740 M 1.000123 1.000414 34.0694974 34.7174821 36.0672253 33191.8 0.0286473 0.95 23.6417236 43.3454393
Chelsea Old church 1712 1842 alpha 1.000092 1.000284 0.0083989 0.0083033 0.0082201 24055.1 0.0000095 0.95 0.0056545 0.0113658
Chelsea Old church 1712 1842 beta 1.000107 1.000363 0.0422444 0.0421520 0.0421527 20068.2 0.0000343 0.95 0.0327982 0.0517568
Chelsea Old church 1712 1842 M 1.000066 1.000214 50.2412943 50.4255236 50.6944550 32126.8 0.0173728 0.95 43.9580757 56.1242381
St. Marylebone 1742 1817 alpha 1.000026 1.000095 0.0125953 0.0125006 0.0123046 29334.6 0.0000102 0.95 0.0092608 0.0160318
St. Marylebone 1742 1817 beta 1.000017 1.000034 0.0420937 0.0420895 0.0423370 23957.1 0.0000291 0.95 0.0331445 0.0508272
St. Marylebone 1742 1817 M 1.000036 1.000085 40.5179648 40.7766676 41.3760128 31991.5 0.0170220 0.95 34.3796076 46.1332104
St. Marylebone Paddington Street north 1772 1853 alpha 1.000045 1.000166 0.0099037 0.0098127 0.0096774 27403.8 0.0000087 0.95 0.0071709 0.0127837
St. Marylebone Paddington Street north 1772 1853 beta 1.000055 1.000206 0.0488613 0.0488575 0.0485839 23270.2 0.0000301 0.95 0.0398523 0.0578266
St. Marylebone Paddington Street north 1772 1853 M 1.000039 1.000116 44.6690555 44.7919466 45.0496301 37001.7 0.0116510 0.95 40.1953904 48.9817326
St. Bride’s lower churchyard 1770 1849 alpha 1.000035 1.000073 0.0061790 0.0061316 0.0059751 14779.1 0.0000071 0.95 0.0045330 0.0078754
St. Bride’s lower churchyard 1770 1849 beta 1.000155 1.000339 0.0510752 0.0510280 0.0511331 11203.6 0.0000422 0.95 0.0423814 0.0598976
St. Bride’s lower churchyard 1770 1849 M 1.000130 1.000460 53.4368072 53.4511152 53.4536777 46992.7 0.0074618 0.95 50.2090353 56.5697935
Sheen’s burial ground 1763 1854 alpha 1.000091 1.000320 0.0129642 0.0128270 0.0124596 28565.8 0.0000128 0.95 0.0089230 0.0173233
Sheen’s burial ground 1763 1854 beta 1.000171 1.000495 0.0353994 0.0353305 0.0350479 24673.6 0.0000300 0.95 0.0262620 0.0446735
Sheen’s burial ground 1763 1854 M 1.000120 1.000420 39.9956498 40.5717091 41.5741951 29050.5 0.0299067 0.95 29.5817256 49.0658033
Bow Baptist Church 1816 1854 alpha 1.000037 1.000121 0.0177742 0.0176655 0.0171967 37363.4 0.0000114 0.95 0.0135868 0.0221462
Bow Baptist Church 1816 1854 beta 1.000013 1.000063 0.0344658 0.0344556 0.0344680 30272.0 0.0000249 0.95 0.0259810 0.0429301
Bow Baptist Church 1816 1854 M 1.000031 1.000063 30.6580796 31.3283020 32.6360138 33171.9 0.0277771 0.95 20.3999444 39.3695617
St. Mary and St. Michael 1843 1853 alpha 1.000523 1.001826 0.0186478 0.0185639 0.0182508 41699.1 0.0000099 0.95 0.0148267 0.0227130
St. Mary and St. Michael 1843 1853 beta 1.000441 1.001467 0.0402140 0.0402172 0.0404972 35162.0 0.0000216 0.95 0.0322916 0.0481568
St. Mary and St. Michael 1843 1853 M 1.000616 1.001944 30.8426109 31.1889790 31.6656994 38394.2 0.0171194 0.95 24.1587401 36.9724139
St. Bride’s crypt (known age) 1740 1853 alpha 1.001301 1.004385 0.0048650 0.0048100 0.0046364 11054.4 0.0000077 0.95 0.0033513 0.0064885
St. Bride’s crypt (known age) 1740 1853 beta 1.001527 1.004999 0.0492998 0.0492831 0.0490777 10841.1 0.0000350 0.95 0.0422819 0.0564716
St. Bride’s crypt (known age) 1740 1853 M 1.000820 1.002819 59.1168993 59.1961001 59.4409448 16528.6 0.0139187 0.95 55.5069567 62.4858268
St. Bride’s crypt (estimates) 1740 1853 alpha 1.000667 1.001933 0.0050596 0.0049986 0.0049298 13764.5 0.0000077 0.95 0.0033634 0.0068603
St. Bride’s crypt (estimates) 1740 1853 beta 1.000585 1.001723 0.0462335 0.0461153 0.0454728 11584.8 0.0000403 0.95 0.0377323 0.0547333
St. Bride’s crypt (estimates) 1740 1853 M 1.000256 1.000830 60.0338767 60.0689768 60.0228465 29593.8 0.0137494 0.95 55.4311154 64.7087860 
kable(wellcome_result_r, caption = "London cemeteries data, corrected for population growth.") %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
London cemeteries data, corrected for population growth.
cemetery start end parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
Bermondsey Abbey 1089 1538 alpha 1.0004384 1.0015608 0.0100569 0.0099338 0.0097741 26240.3 0.0000109 0.95 0.0067655 0.0136223
Bermondsey Abbey 1089 1538 beta 1.0003921 1.0013937 0.0433703 0.0433773 0.0439068 23240.1 0.0000321 0.95 0.0336783 0.0528649
Bermondsey Abbey 1089 1538 M 1.0004266 1.0014866 45.6822436 45.8835839 46.3326136 31446.6 0.0191945 0.95 38.8667009 52.1542950
Bermondsey Abbey 1089 1538 rate 1.0000854 1.0002686 0.0056417 0.0056377 0.0056041 102807.2 0.0000078 0.95 0.0007694 0.0105372
St. Mary Graces 1350 1540 alpha 1.0000932 1.0003161 0.0170437 0.0169434 0.0165866 33968.9 0.0000118 0.95 0.0128337 0.0213373
St. Mary Graces 1350 1540 beta 1.0001339 1.0004049 0.0371500 0.0371640 0.0372066 29663.0 0.0000246 0.95 0.0288233 0.0454699
St. Mary Graces 1350 1540 M 1.0001704 1.0003953 32.6280813 33.0720564 34.0698466 31395.2 0.0239922 0.95 24.0736465 40.3502861
St. Mary Graces 1350 1540 rate 1.0000468 1.0001575 0.0050180 0.0050153 0.0049096 99929.5 0.0000079 0.95 0.0001584 0.0099181
St. Mary Hospital, 1120-1200 1120 1200 alpha 1.0000497 1.0001475 0.0228863 0.0227945 0.0226674 43639.6 0.0000115 0.95 0.0183315 0.0276910
St. Mary Hospital, 1120-1200 1120 1200 beta 1.0000265 1.0000918 0.0379803 0.0379876 0.0382392 42254.5 0.0000186 0.95 0.0304388 0.0454329
St. Mary Hospital, 1120-1200 1120 1200 M 1.0000797 1.0001963 24.9927341 25.4146781 26.3099807 40134.0 0.0201904 0.95 16.8250371 32.3104430
St. Mary Hospital, 1120-1200 1120 1200 rate 0.9999984 1.0000119 0.0028410 0.0028475 0.0030828 117798.6 0.0000072 0.95 -0.0020372 0.0077045
St. Mary Hospital, 1200-1250 1200 1250 alpha 1.0000343 1.0001359 0.0231140 0.0230386 0.0229749 51291.4 0.0000094 0.95 0.0190446 0.0273729
St. Mary Hospital, 1200-1250 1200 1250 beta 1.0000008 1.0000202 0.0397849 0.0397884 0.0399445 50597.0 0.0000158 0.95 0.0328000 0.0467253
St. Mary Hospital, 1200-1250 1200 1250 M 1.0000240 1.0001056 25.4098843 25.7089747 26.2940231 46409.7 0.0150953 0.95 18.8815567 31.4366781
St. Mary Hospital, 1200-1250 1200 1250 rate 1.0000671 1.0002342 0.0127644 0.0127643 0.0128244 107720.3 0.0000076 0.95 0.0078479 0.0175967
St. Mary Hospital, 1250-1400 1250 1400 alpha 1.0000605 1.0000968 0.0162303 0.0161956 0.0161827 23843.8 0.0000076 0.95 0.0139644 0.0185425
St. Mary Hospital, 1250-1400 1250 1400 beta 1.0000277 1.0000352 0.0610335 0.0610352 0.0607921 24621.2 0.0000177 0.95 0.0556105 0.0665374
St. Mary Hospital, 1250-1400 1250 1400 M 1.0000627 1.0001135 33.6949925 33.7284165 33.7756040 26097.4 0.0062172 0.95 31.6778781 35.6134228
St. Mary Hospital, 1250-1400 1250 1400 rate 1.0000509 1.0000976 0.0048756 0.0048759 0.0049617 54702.2 0.0000105 0.95 0.0001435 0.0097655
St. Mary Hospital, 1400-1539 1400 1539 alpha 1.0000461 1.0001787 0.0232316 0.0231524 0.0229215 42351.0 0.0000104 0.95 0.0191346 0.0274639
St. Mary Hospital, 1400-1539 1400 1539 beta 1.0000550 1.0001895 0.0398928 0.0399066 0.0399522 39626.5 0.0000177 0.95 0.0329083 0.0467406
St. Mary Hospital, 1400-1539 1400 1539 M 1.0000630 1.0002150 25.3123997 25.6153914 25.9205036 38299.9 0.0166589 0.95 18.7791532 31.3249516
St. Mary Hospital, 1400-1539 1400 1539 rate 1.0000106 1.0000576 0.0047462 0.0047493 0.0047761 102965.2 0.0000077 0.95 -0.0000588 0.0096690
New Churchyard 1569 1739 alpha 1.0000443 1.0000878 0.0214708 0.0214006 0.0209663 37634.3 0.0000101 0.95 0.0177193 0.0253465
New Churchyard 1569 1739 beta 1.0001137 1.0002395 0.0399080 0.0399144 0.0398191 34807.5 0.0000187 0.95 0.0330545 0.0467203
New Churchyard 1569 1739 M 1.0001096 1.0002228 27.3135812 27.5906580 28.2926994 34445.2 0.0165348 0.95 21.1340430 32.9495481
New Churchyard 1569 1739 rate 1.0000195 1.0000586 0.0075658 0.0075639 0.0075793 87658.4 0.0000084 0.95 0.0026693 0.0124236
St. Benet Sherehog 1670 1740 alpha 1.0001384 1.0005211 0.0135181 0.0133737 0.0130458 33103.2 0.0000123 0.95 0.0093450 0.0180349
St. Benet Sherehog 1670 1740 beta 1.0002094 1.0006563 0.0377790 0.0377933 0.0378383 29389.9 0.0000283 0.95 0.0282675 0.0472846
St. Benet Sherehog 1670 1740 M 1.0001248 1.0004113 38.9022566 39.3863806 40.2827832 33435.8 0.0255764 0.95 29.5999300 47.4994365
St. Benet Sherehog 1670 1740 rate 1.0000249 1.0001064 0.0054268 0.0054189 0.0052620 113812.2 0.0000074 0.95 0.0005475 0.0103210
Chelsea Old church 1712 1842 alpha 1.0001480 1.0002573 0.0064751 0.0063650 0.0061572 23987.2 0.0000085 0.95 0.0040732 0.0090999
Chelsea Old church 1712 1842 beta 1.0002599 1.0005036 0.0453886 0.0454175 0.0458495 19708.4 0.0000382 0.95 0.0347547 0.0557406
Chelsea Old church 1712 1842 M 1.0000299 1.0000809 55.0713758 55.1425610 55.3075641 43979.1 0.0148353 0.95 48.9491500 61.2053202
Chelsea Old church 1712 1842 rate 1.0000055 1.0000176 0.0075938 0.0075935 0.0077701 91647.9 0.0000082 0.95 0.0027064 0.0124833
St. Marylebone 1742 1817 alpha 1.0002096 1.0006937 0.0101454 0.0100403 0.0096732 29247.2 0.0000094 0.95 0.0071183 0.0133209
St. Marylebone 1742 1817 beta 1.0001959 1.0007254 0.0451219 0.0451403 0.0452213 25685.0 0.0000291 0.95 0.0358427 0.0541354
St. Marylebone 1742 1817 M 1.0001775 1.0005507 45.0630043 45.2182975 45.4917442 36807.9 0.0148453 0.95 39.3682842 50.5105928
St. Marylebone 1742 1817 rate 1.0000264 1.0001090 0.0074627 0.0074645 0.0074099 101468.4 0.0000078 0.95 0.0025035 0.0122621
St. Marylebone Paddington Street north 1772 1853 alpha 1.0000658 1.0001793 0.0067701 0.0066902 0.0064467 28487.4 0.0000068 0.95 0.0046537 0.0090813
St. Marylebone Paddington Street north 1772 1853 beta 1.0002920 1.0009451 0.0540540 0.0540386 0.0537952 25941.0 0.0000294 0.95 0.0447935 0.0633352
St. Marylebone Paddington Street north 1772 1853 M 1.0000059 1.0000339 50.5697372 50.5848711 50.6009045 50608.7 0.0096803 0.95 46.2707037 54.8331587
St. Marylebone Paddington Street north 1772 1853 rate 1.0000299 1.0001073 0.0134441 0.0134422 0.0134743 101318.9 0.0000078 0.95 0.0085652 0.0183044
St. Bride’s lower churchyard 1770 1849 alpha 1.0004322 1.0014789 0.0038814 0.0038350 0.0037138 15446.1 0.0000053 0.95 0.0026400 0.0051734
St. Bride’s lower churchyard 1770 1849 beta 1.0010900 1.0037600 0.0576544 0.0576445 0.0577487 12270.4 0.0000429 0.95 0.0483361 0.0669182
St. Bride’s lower churchyard 1770 1849 M 1.0001688 1.0005250 59.0047132 58.9475585 58.8194768 40939.7 0.0095875 0.95 55.2666792 62.8844643
St. Bride’s lower churchyard 1770 1849 rate 1.0000394 1.0001612 0.0132584 0.0132596 0.0130524 51199.2 0.0000110 0.95 0.0083901 0.0181456
Sheen’s burial ground 1763 1854 alpha 1.0000293 1.0000680 0.0084873 0.0083593 0.0081090 30274.8 0.0000097 0.95 0.0053490 0.0118633
Sheen’s burial ground 1763 1854 beta 1.0000180 1.0000412 0.0406644 0.0406625 0.0407175 27222.0 0.0000314 0.95 0.0305497 0.0508194
Sheen’s burial ground 1763 1854 M 1.0000358 1.0000988 50.5692812 50.7601405 51.1279864 39066.8 0.0202627 0.95 42.5612107 58.2859301
Sheen’s burial ground 1763 1854 rate 0.9999938 0.9999965 0.0131468 0.0131420 0.0130719 103861.1 0.0000077 0.95 0.0082953 0.0180378
Bow Baptist Church 1816 1854 alpha 1.0001794 1.0006411 0.0110382 0.0109321 0.0107885 42063.6 0.0000081 0.95 0.0078918 0.0143754
Bow Baptist Church 1816 1854 beta 1.0000875 1.0003385 0.0407854 0.0408127 0.0410007 36030.6 0.0000239 0.95 0.0318381 0.0496526
Bow Baptist Church 1816 1854 M 1.0001823 1.0006454 43.9628080 44.1658715 44.3668412 48157.6 0.0152389 0.95 37.3316415 50.3647476
Bow Baptist Church 1816 1854 rate 1.0000471 1.0001859 0.0174518 0.0174583 0.0173503 105037.5 0.0000077 0.95 0.0126640 0.0224305
St. Mary and St. Michael 1843 1853 alpha 1.0000453 1.0000833 0.0122773 0.0121962 0.0121064 44999.3 0.0000075 0.95 0.0092535 0.0154473
St. Mary and St. Michael 1843 1853 beta 1.0001569 1.0004401 0.0459527 0.0459641 0.0460400 42305.4 0.0000203 0.95 0.0378064 0.0541617
St. Mary and St. Michael 1843 1853 M 1.0000225 1.0000500 40.6854815 40.8011992 41.0795546 51268.0 0.0110280 0.95 35.7249958 45.4780928
St. Mary and St. Michael 1843 1853 rate 1.0000285 1.0000843 0.0176492 0.0176411 0.0176163 114015.4 0.0000074 0.95 0.0127677 0.0225102
St. Bride’s crypt (known age) 1740 1853 alpha 1.0004443 1.0013905 0.0032673 0.0032272 0.0031669 12848.3 0.0000049 0.95 0.0022166 0.0043711
St. Bride’s crypt (known age) 1740 1853 beta 1.0004021 1.0012201 0.0548600 0.0548491 0.0546809 12567.4 0.0000327 0.95 0.0476639 0.0620221
St. Bride’s crypt (known age) 1740 1853 M 1.0002073 1.0007301 63.6024120 63.6337709 63.7592027 32254.3 0.0081643 0.95 60.6589371 66.4269445
St. Bride’s crypt (known age) 1740 1853 rate 0.9999985 1.0000287 0.0100125 0.0100126 0.0100097 119697.3 0.0000003 0.95 0.0098169 0.0102088
St. Bride’s crypt (estimates) 1740 1853 alpha 1.0004308 1.0015894 0.0034406 0.0033730 0.0032441 14094.3 0.0000063 0.95 0.0020379 0.0049290
St. Bride’s crypt (estimates) 1740 1853 beta 1.0008845 1.0032184 0.0491434 0.0491562 0.0493642 11007.9 0.0000520 0.95 0.0384382 0.0598310
St. Bride’s crypt (estimates) 1740 1853 M 1.0000909 1.0001930 66.5116525 66.3845608 66.2563248 35656.6 0.0160904 0.95 60.7073912 72.6176158
St. Bride’s crypt (estimates) 1740 1853 rate 1.0000276 1.0001275 0.0099942 0.0099897 0.0097761 42873.4 0.0000121 0.95 0.0050317 0.0148290

Figure 6: Estimated modal ages from written sources and osteological data compared, upper panel: without population growth correction, lower panel: with population growth correction. Horizontal bars indicate the time span the data point covers. Vertical bars indicate 95% HDI for credible ranges and are only displayed for small n, i.e. English Peers, Christ Church monks and osteological data.

# get symbols & colors from palette alphabet (max n = 26), alt. glasbey (32), polychrome(36)
plotcolors<-palette.colors(palette = 'alphabet')
plotsymbols<-c(17,18,15)

# MOLA Welcome data without correction of population growth
english_wellcome <- rbind(english_mortality_prep, wellcome_prep)

# slight modifications
english_wellcome <- english_wellcome %>%
  mutate(data = factor(data, levels = unique(data))) %>%
  mutate(source = gsub('written','England & Wales written', source)) %>%
  mutate(source = gsub('osteological','London osteological', source)) %>%
  mutate(source = ifelse(data=="London 1728-1840","London written",source)) %>%
  mutate(source = factor(source, levels = c('England & Wales written', 'London written', 
                         'London osteological'))) %>%
  mutate(start = as.numeric(start)) %>%
  mutate(end = as.numeric(end)) %>%
  mutate(year = ifelse(is.na(year), (start + end)/2, substr(year, 2,5))) %>%
  mutate(year = as.numeric(year))

ggplot(english_wellcome, aes(x = year, y = M, colour = data, shape = source) ) + 
  ylab("modal age & HDI low - HDI high")  + 
  xlab("year (from - to)") + ylim(2, 75) + theme_light() +
  scale_color_manual(values=unname(plotcolors)) +
  scale_shape_manual(values=plotsymbols) +
  geom_smooth(color = "dark grey", method = 'loess', formula = 'y ~ x') +
  geom_errorbar(aes(ymin = HDIlow, ymax=  HDIhigh), width=0, colour = "dark grey") +
  geom_errorbarh(aes(xmax = start, xmin = end, height = 1)) +
  geom_point(size= 2 ) + 
  guides(size = "none",colour=guide_legend(ncol=1)) +
  scale_x_continuous (breaks = seq(1200, 1800, by = 200)) +
  theme(legend.position="none") -> english_wellcome_plot

# MOLA Welcome data with correction of population growth (_r)
english_wellcome_r <- rbind(english_mortality_prep_r, wellcome_prep_r)

# slight modifications
english_wellcome_r <- english_wellcome_r %>%
  mutate(data = factor(data, levels = unique(data))) %>%
  mutate(source = gsub('written','England & Wales written', source)) %>%
  mutate(source = gsub('osteological','London osteological', source)) %>%
  mutate(source = ifelse(data=="London 1728-1840","London written",source)) %>%
  mutate(source = factor(source, levels = c('England & Wales written', 'London written', 
                         'London osteological'))) %>%
  mutate(start = as.numeric(start)) %>%
  mutate(end = as.numeric(end)) %>%
  mutate(year = ifelse(is.na(year), (start + end)/2, substr(year, 2,5))) %>%
  mutate(year = as.numeric(year))

ggplot(english_wellcome_r, aes(x = year, y = M, colour = data, shape = source) ) + 
  ylab("modal age (corrected for population growth)")  + 
  xlab("year (from - to)") + ylim(2, 75) + theme_light() +
  scale_color_manual(values=unname(plotcolors)) +
  scale_shape_manual(values=plotsymbols) +
  geom_smooth(color = "dark grey", method = 'loess', formula = 'y ~ x') +
  geom_errorbar(aes(ymin = HDIlow, ymax=  HDIhigh), width=0, colour = "dark grey") +
  geom_errorbarh(aes(xmax = start, xmin = end, height = 1)) +
  geom_point(size= 2 )+ 
  guides(size = "none",colour=guide_legend(ncol=1)) +
  scale_x_continuous (breaks = seq(1200, 1800, by = 200)) -> english_wellcome_plot_r

# get the legend and remove it afterwards 
ewp_legend <- get_legend(english_wellcome_plot_r)
english_wellcome_plot_r <- english_wellcome_plot_r + theme(legend.position="none")

# build the image
grid::grid.newpage()
ewp<-plot_grid(english_wellcome_plot, english_wellcome_plot_r, ncol=1)
modal_ages_plot <- plot_grid(ewp, ewp_legend, ncol = 2, rel_widths = c(.75, .25))

# Save the finished map object
ggsave(
  filename = "fig06_modal_ages_plot.pdf",
  width = 11, height = 8.5,
  plot = modal_ages_plot, 
  device = "pdf",
  path = "documented"
)

plot(modal_ages_plot)

The following data overview is build during pre-processing in ./chapter_04_results/Wellcome_DB.R and saved to a textfile (sep = \t).

Table 2: Major cemeteries of London, without and with (r) compensation of population growth. beta – Gompertz beta parameter; M – modal age; ex20 – life expectancy at age 20; ex25 – life expectancy at age 25. Ranges computed with credible HDIs of 95%.

kable(wellcome_overview_all) %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
cemetery beta beta_range M M_range ex20 ex25 r_beta r_beta_range r_M r_M_range r_ex20 r_ex25
Bermondsey Abbey 0.0414 0.0319-0.0504 42.6 34.7-48.4 25.5 22.7 0.0439 0.0337-0.0529 46.3 38.9-52.2 27.1 24.1
Bow Baptist Church 0.0345 0.026-0.0429 32.6 20.4-39.4 22.7 20.4 0.0410 0.0318-0.0497 44.4 37.3-50.4 26.9 24.0
Chelsea Old church 0.0422 0.0328-0.0518 50.7 44-56.1 30.4 27.3 0.0458 0.0348-0.0557 55.3 48.9-61.2 33.1 29.6
New Churchyard 0.0365 0.0299-0.0432 22.5 13.7-27.9 17.0 15.0 0.0398 0.0331-0.0467 28.3 21.1-32.9 18.5 16.3
Sheen’s burial ground 0.0350 0.0263-0.0447 41.6 29.6-49.1 27.3 24.6 0.0407 0.0305-0.0508 51.1 42.6-58.3 31.3 28.2
St. Benet Sherehog 0.0353 0.0265-0.0446 36.1 23.6-43.3 23.7 21.2 0.0378 0.0283-0.0473 40.3 29.6-47.5 25.4 22.7
St. Bride’s crypt (estimates) 0.0455 0.0377-0.0547 60.0 55.4-64.7 36.8 33.2 0.0494 0.0384-0.0598 66.3 60.7-72.6 41.2 37.3
St. Bride’s crypt (known age) 0.0491 0.0423-0.0565 59.4 55.5-62.5 35.7 32.0 0.0547 0.0477-0.062 63.8 60.7-66.4 38.4 34.5
St. Bride’s lower churchyard 0.0511 0.0424-0.0599 53.5 50.2-56.6 31.0 27.5 0.0577 0.0483-0.0669 58.8 55.3-62.9 34.6 30.7
St. Mary Graces 0.0349 0.0267-0.0427 29.1 17.8-36.2 20.8 18.6 0.0372 0.0288-0.0455 34.1 24.1-40.4 22.2 19.8
St. Mary Hospital, 1120-1200 0.0366 0.0289-0.0437 23.6 12.9-29.7 17.4 15.4 0.0382 0.0304-0.0454 26.3 16.8-32.3 18.0 15.9
St. Mary Hospital, 1200-1250 0.0355 0.0289-0.0424 17.8 7.7-24.3 15.7 13.8 0.0399 0.0328-0.0467 26.3 18.9-31.4 17.4 15.3
St. Mary Hospital, 1250-1400 0.0577 0.0529-0.0634 32.0 30-33.6 16.0 13.4 0.0608 0.0556-0.0665 33.8 31.7-35.6 16.5 13.8
St. Mary Hospital, 1400-1539 0.0374 0.0307-0.0443 22.2 13.7-27.8 16.7 14.7 0.0400 0.0329-0.0467 25.9 18.8-31.3 17.4 15.3
St. Mary and St. Michael 0.0405 0.0323-0.0482 31.7 24.2-37 20.0 17.6 0.0460 0.0378-0.0542 41.1 35.7-45.5 23.4 20.6
St. Marylebone 0.0423 0.0331-0.0508 41.4 34.4-46.1 24.5 21.7 0.0452 0.0358-0.0541 45.5 39.4-50.5 26.7 23.7
St. Marylebone Paddington Street north 0.0486 0.0399-0.0578 45.0 40.2-49 25.4 22.4 0.0538 0.0448-0.0633 50.6 46.3-54.8 28.8 25.4 
write.table(wellcome_overview_all, file = "./documented/table02_osteological_estimates.txt", sep="\t", quote = FALSE)

Data are hard coded in the code. Sources: Miles, Powers, et al. (2008), 97–103 table 32 (St Marylebone); Henderson et al. (2015), 81 (St Marylebone north of Paddington street)

source("./lifetables_processing/Marylebone.R")
kable(Marylebone_ranges, caption = "St Marylebone, corrected with population growth rate of 2.75 per-cent.") %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
St Marylebone, corrected with population growth rate of 2.75 per-cent.
parameter modes HDI.ranges
Marylebone beta 0.0527 0.0433-0.0619
Marylebone M 54.4880 49.6-59.3
Marylebone north beta 0.0593 0.0499-0.0685
Marylebone north M 55.3931 51.4-59.9

The following plot is build in ./lifetables_processing/stbrides_crypt.R within the if-statement on runCodeNew (s. data limitations above).

Figure 7: St. Bride’s Crypt. Density of actual ages and Bayesian model of Gompertz distribution of actual ages and osteological estimates (without correction for population growth).

plot(stbrides_crypt_plot)

Figure 8: Simulation of population increase with known age-at-death and Maximum Likelihood Estimation (MLE) (top four) and osteological estimates, Bayesian model and including rate of increase (bottom four).

if (runCodeNew){
  set.seed(3673)
  lt_sim_list <- list()
  for(k in 1:4) {
    lt_sim <- lt.MC.Gomp(pop_start = c(10000, 1000, 500, 200, 100), 
                         pop_inc = c(-0.02, 0, 0.005, 0.01, 0.02), 
                         years = 200,   
                         obs_start = 150, 
                         obs_end = 200, 
                         beta = (k + 2)/100, 
                         bayes = TRUE)
    lt_sim_list[[k]] <- lt_sim
  }
  
  # saves results in Rda-object
  save(lt_sim_list, file = file.path(".", saveFileDir, "lt_sim_list.Rda") )
}
load(file.path(".", saveFileDir, "lt_sim_list.Rda") )

lt_sim_plot_list <- list()
for (i in 1:4) {
lt_sim_plot_list[[i]] <- ggplot(lt_sim_list[[i]], aes(y = surv_Gompertz_shape, x = as.factor(pop_inc))) + 
  geom_boxplot()  + 
  ggtitle(paste0("\u03B2: ", (i + 2)/100) ) +
  ylab("Gompertz \u03B2 (MLE)") + xlab("population increase") + 
  theme(plot.margin = unit(c(0,0.5,0.5,0), "cm"),
        plot.title = element_text(size = 12),
        axis.title = element_text(size = 10),
        axis.text = element_text(size = 8)) + theme_light()
lt_sim_plot_list[[i + 4]] <-   ggplot(lt_sim_list[[i]], aes(y = bayes_gomp_b, x = as.factor(pop_inc)) ) + 
  geom_boxplot()  + 
  ggtitle(paste0("\u03B2: ", (i + 2)/100) ) +
  ylab("Gompertz \u03B2 (Bayes)") + xlab("population increase") + 
  theme(plot.margin = unit(c(0,0.5,0.5,0), "cm"),
              plot.title = element_text(size = 12),
              axis.title = element_text(size = 10),
              axis.text = element_text(size = 8)) + theme_light()
}

lt_sim_plots <- gridExtra::grid.arrange (grobs = lt_sim_plot_list, ncol = 4,
                                         top = textGrob("Original Gompertz\n", 
                                                        gp=gpar(fonsize = 14)))

# Save the finished map object
ggsave(
  filename = "fig08_lt_sim_plots.pdf",
  width = 11.5, height = 8,
  plot = lt_sim_plots, 
  device = cairo_pdf,
  path = "documented"
)

Supporting information

The chapter ‘Supporting information’ provides details about the London cemeteries included in the study, the Gompertz parameters of the Coale & Demeny life tables, and the simulations and their results.

The Coale & Demeny life tables

Calculation of the lowest \(\beta\)-value for any of the Coale & Demeny life tables (Coale & Demeny (1983)) which is 0.0391 (the female table “West”, level 1).

source("./chapter_supplement/coale_demeny_life_tables_gompertz.R")
min(gompertz_df$Gompertz_shape)
## [1] 0.03913138

Simulations

Figure S1: Comparing expected and estimated Gompertz \(\beta\)-values by different algorithms with known age-at-death (n = 1,000).

source("./chapter_supplement/simulations_run.R")
gridExtra::grid.arrange(grobs = plot_list_shapes, ncol = 3)

Figure S2: Difference between expected and estimated Gompertz \(\beta\)-values by different algorithms with known age-at-death (n = 1,000).

source("./chapter_supplement/simulations_run.R")
gridExtra::grid.arrange(grobs = plot_list_diff, ncol = 3)

Table T1: Root mean square errors (RMSE) for different formulas for fitting known age-at-death, in ascending order.

# table of RMSEs
kable(rmse_result[order(rmse_result$RMSE) ,]) %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
method RMSE NAs
11 Bayes (5y-cat) 0.0045054 0
10 Bayes 0.0045342 0
7 MLE 0.0047464 0
4 survival 0.0047465 0
12 Bayes (10y-cat) 0.0048206 0
8 MLE (5y-cat) 0.0048251 0
5 survival (5y-cat) 0.0048980 0
1 OLS 0.0049008 545
9 MLE (10y-cat) 0.0051441 0
2 WOLS 0.0060401 0
3 WNLS 0.0061083 14
6 survival (10y-cat) 0.0067095 0

Figure S3: Comparison of methods to estimate the original Gompertz \(\beta\) from simulated data with anthropological age categories (n = 1,000).

source("./chapter_supplement/simulations_run.R")
gridExtra::grid.arrange(grobs = plot_list_estim_shapes, ncol = 2)

Table T2: Root mean square errors in different methods to estimate the original Gompertz \(\beta\) from simulated data with anthropological age categories, in ascending order.

# table of RMSEs
kable(rmse_estim_result[order(rmse_estim_result$RMSE) ,]) %>%
  kableExtra::kable_styling(latex_options = "HOLD_position")
method RMSE NAs
6 Bayes (cat) 0.0099026 0
7 MLE_wo_OL 0.0202114 71
1 OLS 0.0243214 442
3 WNLS 0.0293842 73
2 WOLS 0.0328083 2
5 MLE (cat) 0.0761568 0
4 survival (cat) 0.4731442 0

Figure S4: Bayesian model of simulated data with anthropological age categories and random error in “age estimation.” Difference of estimated to original Gompertz \(\beta\) in relation to original \(\beta\) (left) and sample size (right).

#source("./chapter_supplement/simulations_run.R")
gridExtra::grid.arrange(grobs = plot_list_bayes_diff, ncol = 2)

Table T3: Bayesian model with simulated data-set to compare the impact of thinning and additional steps. n = 500, Gompertz \(\beta\) = 0.05.

source("./chapter_supplement/bayes_complete.R") # can take a few minutes
kable (bayes_complete) %>%
  kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
mode thinning steps parameter PSRF Point est. PSRF Upper C.I. Mean Median Mode ESS MCSE HDImass HDIlow HDIhigh
known_age 1 10000 a 1.003210 1.006108 0.0028582 0.0028441 0.0027725 462.7 0.0000154 0.95 0.0022403 0.0035193
known_age 1 10000 b 1.001893 1.003920 0.0480363 0.0480265 0.0481745 488.6 0.0000947 0.95 0.0440097 0.0520917
known_age 1 10000 M 1.001259 1.003216 73.8375371 73.8501409 73.6934420 930.5 0.0357533 0.95 71.6915433 75.9608132
known_age 20 100000 a 1.000011 1.000109 0.0028495 0.0028327 0.0027934 71982.2 0.0000013 0.95 0.0022163 0.0035260
known_age 20 100000 b 1.000005 1.000090 0.0480993 0.0480962 0.0483082 71181.0 0.0000080 0.95 0.0438344 0.0521777
known_age 20 100000 M 1.000000 1.000078 73.8543153 73.8768307 73.9884330 84071.3 0.0037849 0.95 71.6339091 75.9294081
estimation 1 10000 a 1.007384 1.023678 0.0028312 0.0028026 0.0027942 167.5 0.0000382 0.95 0.0019049 0.0038193
estimation 1 10000 b 1.011691 1.038693 0.0510970 0.0508290 0.0503803 86.5 0.0005942 0.95 0.0404465 0.0624583
estimation 1 10000 M 1.005548 1.017117 71.9242579 71.9119671 72.0531786 392.2 0.1119194 0.95 67.6950056 76.3291669
estimation 20 100000 a 1.000247 1.000941 0.0027769 0.0027509 0.0027034 29177.9 0.0000026 0.95 0.0019290 0.0036726
estimation 20 100000 b 1.000354 1.001342 0.0516959 0.0514776 0.0502964 20843.0 0.0000356 0.95 0.0421542 0.0619696
estimation 20 100000 M 1.000091 1.000334 71.8362699 71.7754410 71.6155191 45976.8 0.0102799 0.95 67.6297829 76.2104655

References

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  1. Institute for Prehistoric and Protohistoric Archaeology - Kiel University ↩︎

  2. Institute for Prehistoric and Protohistoric Archaeology - Kiel University, ↩︎

  3. Institute for Prehistoric and Protohistoric Archaeology - Kiel University, ↩︎